Mathematics

CONTENTS

General Mathematical Resources
Puzzles
Factoids and Oddities
Worksheets, Example sheets
Calculus

Paul Kunkel's Whistler Alley Mathematics. Paul says, "This is a collection of math topics prepared by me. It is my best stuff. Please, visit."

Graeme's comment: very interesting geometrical things, especially involving generalized circles and inversion geometry, and some helpful cut-the-knot-like applets. Well worth a visit.

Mudd Math Fun Facts. This is mathematics made interesting.

What's Special about this Number? a factoid about just about every number smaller than 220 and a whole lot of numbers between 220 and 10,000.

The Fibonacci Sequence Module M -- including a proof that given any integer m, infinitely many Fibonacci numbers are divisible by m.

and other mathematical constants:

http://oldweb.cecm.sfu.ca/pi/pi.html

http://www.cecm.sfu.ca/~pborwein/PISTUFF/Apistuff.html

http://www.mathsoft.com/mathsoft_resources/mathsoft_constants/ lists a bunch of constants, but even more are listed by

http://pauillac.inria.fr/algo/bsolve/constant/constant.html , which lists these constants:

Well-known constants: Zero, 0; One, 1; Imaginary unit,; Pythagoras' constant,; Golden mean,; Natural logarithmic base, e; Archimedes' constant,; Euler-Mascheroni constant,; Apéry's constant,; Catalan's constant, G; Khintchine's constant; Feigenbaum constants; Madelung's constant; Chaitin's constant

Constants associated with Number Theory: Hardy-Littlewood constants; Meissel-Mertens constants; Euler gamma function constants; Landau-Ramanujan constant; Sierpinski's constant; Brun's constant; Artin's constant; Linnik's constant; Hafner-Sarnak-McCurley constant; Gauss-Kuzmin-Wirsing constant; Stolarsky-Harborth constant; Porter's constant; Glaisher-Kinkelin constant; Fransén-Robinson constant; Alladi-Grinstead constant; Niven's constant; Backhouse's constant; Mills' constant; Stieltjes constants; Liouville-Roth constants; Diophantine approximation constants; Erdös' reciprocal sum constants; Abundant numbers density constant; Self-numbers density constant; Ramanujan-Soldner constant; Cameron's sum-free set constants; Euler totient function asymptotic constants; Pisot-Vijayaraghavan-Salem constants; Nielsen-Ramanujan constants; Triple-free set constants; De Bruijn-Newman constant; Komornik-Loreti constant; Freiman's constant; Erdös-Lebensold constant; Cahen's constant; Hall-Montgomery constant; Fast matrix multiplication constants; Erdös' sum-distinct set constant; Vallée's constant; Pell-Stevenhagen constants

Constants associated with Analytic Inequalities: Shapiro's cyclic sum constant; Carlson-Levin constants; Landau-Kolmogorov constants; Hilbert's constants; Copson-de Bruijn constants; Wirtinger-Sobolev isoperimetric constants; Whitney-Mikhlin extension constants; Korn constants; Kneser-Mahler polynomial constants; Grothendieck's constants; Du Bois Reymond's constants; Steinitz constants; Young-Fejér-Jackson constants; Van der Corput's constant

Constants associated with the Approximation of Functions: Wilbraham-Gibbs constant; Lebesgue constants; Favard constants; Bernstein's constant; The "one-ninth" constant; Laplace limit constant; Integer Chebyshev constant

Constants associated with Enumerating Discrete Structures: Abelian group enumeration constants; Pythagorean triple constants; Rényi's parking constants; Golomb-Dickman constant; Lengyel's constant; Otter's tree enumeration constants; Pólya's random walk constants; Self-avoiding-walk connective constants; Feller's coin tossing constants; Hard square entropy constant; Binary search tree constants; Digital search tree constants; Quadtree constants; Extreme value constants; Pattern-free word constants; Takeuchi-Prellberg constant; Percolation cluster density constants; Klarner's lattice animal constant; Lenz-Ising constants; 2D Monomer-dimer constant; 3D dimer constant; Lieb's square ice constant; Odlyzko-Rains constants; Tutte-Beraha constants

Constants associated with Functional Iteration: Gauss' lemniscate constant; Grossman's constant; Plouffe's constant; Lehmer's constant; Iterated exponential constants; Continued fraction constants; Infinite product constants; Quadratic recurrence constants; Conway's constant

Constants associated with Complex Analysis: Bloch-Landau constants; Masser-Gramain constant; John constant; Hayman constants; Littlewood-Clunie-Pommerenke constants; Whittaker-Goncarov constants; Grötzsch ring constants

Constants associated with Geometry: Geometric probability constants; Circular coverage constants; Universal coverage constants; Hermite's constants; Tammes' constants; Calabi's triangle constant; DeVicci's tesseract constant; Graham's hexagon constant; Traveling salesman constants; Steiner tree constants; Moving sofa constant; Beam detection constant; Heilbronn triangle constants; Kakeya-Besicovitch constants; Moser's worm constant; Rectilinear crossing constant; Maximum inradius constants; Apollonian packing constant; Magic geometric constants

Relevant Links: Inverse Symbolic Calculator and Integer Relations (CECM); Numbers, Constants and Computation, by X. Gourdon and P. Sebah; Recognizing Numerical Constants, by D. H. Bailey and S. Plouffe; What is a Number?, by A. Bogomolny; What is a Closed-Form Number?, by T. Y. Chow; How Many Fundamental Physical Constants are There?, by J. Baez; On the Random Character of Fundamental Constant Expansions, by D. H. Bailey and R. E. Crandall; University of Tennesse Mathematics Archives Page about Numbers; Math Forum Internet Mathematics Library Page about Numbers; Power Sums of Complex Numbers; Polynomial Optimization Over an Ellipse; Yahoo Page about Numbers

Geometry, and other mathematics:
Math Words and Other Words of Interest,

by Pat Ballew

www.pballew.net/etyindex.html

The Anti-Divisor

...and other mathematics

by Jon Perry

www.users.globalnet.co.uk/~perry/maths/index.htm

The University of Tennessee at Martin

The Largest Known Primes Database	The "Guinness book" of prime number records! Includes the 5000 largest known primes and smaller ones of selected forms (one-page summary) updated hourly!
Prime Links	Hundreds of links to other prime resources including history, programs, theory and more!
Lists of Primes	The first 1,000 primes. The first 15,000,000 primes. Top 20 records (e.g., twin primes, Mersenne primes...) Lists of 300 digit primes. And much more!
Finding primes, proving primality	Explains the mathematical theory behind how these record primes are found.
How many are there?	Infinity, but How Big of an Infinity?
The Largest Known Prime by Year: A Brief History	Discusses how big have the largest known primes been historically (and uses that to predict how big they will be)!

More prime resources

Conjectures and Open Problems
A short list of conjectures and open problems relating to primes.
The Riemann Hypothesis
One of the most important conjectures in prime number theory. When (and if) it is proven, many of the bounds on prime estimates can be improved and primality proving can be simplified.
Prime Curios!
"Prime Curios!" is an exciting collection of curiosities, wonders and trivia related to prime numbers.
Prime Glossary
Definition of terms related to prime numbers and primality.
Check a Number's Primality
A simple routine to check most small numbers for primality.
Important Discovery: "Primes in P"
Primality can be tested in deterministic polynomial time--this is of great theoretical value; but of questionable practical value.